Stagger damped tuned amplifier



7 g 1949. H. WALLMAN D 2,480,205

STAGGER DAMPED TUNED AMPLIFIER Filed Sept. 14, 1945 FIG. 3

DOUBLE TUNED CIRCUIT LOADED ONE ONLY Q FIXED h VARIABLE FIG. 4

DOUBLE TUNED cmcun' LOADED ONE ONLY 4E FIXED Q VARIABLE 4.0 '35 -3 .O -25 2.0-1.5 L0 -.5 O .5 L0 L5 2.0 2.5 3.0 35 4.0

Av ans-m) I INVENTOR. F? A 5 I HENRY WALLMAN ATTORNEY.

Patented Aug. 30, 1949 UNITED STATES PATENT OFFICE STAGGER DAMPED TUNED AMPLIFIER Application September 14, 1945, Serial No. 616,371

Claims. 1

This invention relates in general to electrical circuits and more particularly to amplifiers containin a plurality of stages.

Amplifiers that are used to amplify pulses so as to maintain the same shape in the output voltage as in the applied voltage must amplify a wide band of frequencies with very nearly uniform gain throughout the band. When amplifiers must have high gain characteristics it is difficult to maintain wide bandwidth characteristics as the two functions are usually related in such a manner that if one is increased, the other is decreased. Furthermore, it can be shown that the problem becomes even more difiicult when multiple stages are cascaded. The gain of a multistage amplifier consisting of 11 identical stages is the gain of one stage to the nth power. It can be also shown that the overall bandwidth of n stages of a single-tuned amplifier is times the bandwith of one stage. Whereas, the overall bandwith of n stages of a double-tuned amplifier is tuned I. F. amplifier would have .803 times the bandwidth of one stage.

employed in the circuit so that the gain and bandwidth desired may be realized with a mini- In certain types of radio object locating device s, l

it is necessary to employ receivers that will faithfully detect and amplify pulses having a duration mum amount of experimentation and adjustment.

Other objects, features, and advantages of this invention will Suggest themselves to those skilled in the art and will become'apparent from the following description of the inventiontaken in connection with the accompanying drawings in which: Y

Fig. 1 is a diagram of a double-tuned circuit loaded on one side only;

Fig. 2 is a diagram of a double-tuned circuit illustrating its use as a coupling network between successive vacuum tubes;

Fig. 3 is a graph showin certain relative selectivity curves for a double-tuned circuit loaded on one side only;

Fig. 4 is a graph showing other relative selectivity curves having a double-tuned circuit loaded on one side only; and

Fig. 5 is a graph of a typical selectivity curve.

Referring now more particularly to Fig. 1 which shows a double-tuned circuit loaded on one side only, resistor Rp represents the equivalent parallel resistance of the primary circuit. Capacitor Cp represents the equivalent parallel capacitance of the primary circuit. Inductance Lp represents the euuivalent parallel inductance of the primary circuit and 7c is the coefiicient of coupling between the primary circuit and the secondary circuit. Inductance L5 represents the equivalent parallel inductance of the secondary circuit and capacitor Cs represents the equivalent parallel capacitance of the secondary circuit.

It can be shown that the voltage across the secondary capacitor (Cs) divided by the voltage applied in series with a primary circuit may be of the order of one-tenthmicrosecond and the D SSBd a5 amplification must be extremely large. It is conimon practice under these conditions to use a receiver having a large number of I. F. stages.

There is thus presented the problem of obtaining high-gain characteristics simultaneously with wide band characteristics.

1 It is therefore anobject of this invention to provide a means for obtaining wide bandwidth in an amplifier and simultaneously maintaining high gain per stage and overall amplification. It is further an object of this invention to provide a method of choosing the values of the elements Q,,= for primary circuit L for secondary circuit It =coefficient of coupling L,=total inductance of primary circuit L =total inductance of secondary circuit Equation A is a basic equation for a double-tuned circuit and appears on page 155 of the Radio Engineers Handbook by Frederick E. Terman, published by McGraw-Hill Book Co., Inc., in 1943.

To simplify mathematical computation the circuit of Fig. 1 is considered when 1:1, L11=1, :1, and Ls=1, When k=coefiicient of coupling then Assuming Qp to be large and that one ampere is applied through the primary 141:, and also making the approximation that Equation A may be reduced to It is observed that the secondary voltage at the bandwidth center is entirely independent of Qp and depends only on the coefiicient of coupling 70. The absolute value of Equation B is when coefficient of coupling= bandwidth at transitional coupling center frequency The voltage at the center frequency is hence, the product of voltage times Aw=1 for transitional coupling. But the total capacity of the circuit is 2; this leads to the well-known result that the gain times bandwidth product of a double-tuned circuit, loaded on one side only, at transitional couplin is twice that of a singletuned circuit.

For fixed Q, transitional coupling is illustrated y 4 Fig. 3 shows relative selectivity curves for 700:5, .707, 1, 1.414, 2. The ordinate value 1 denotes a voltage of Qx/2 and the abscissa value 1 denotes a value for :c of

Fig. 4 shows relative selectivity curves for The ordinate value 1 denotes a voltage of and the abscissa value 1 denotes a value for x of 7c.

It is also noted that with k fixed and Q variable the voltage at center-frequency is constant; this is indeed evident from Equation B.

The basic idea of this invention is to have successive coupling stages of an I. F. amplifier identical except for their damping resistors so that some will be overcoupled and some undercoupled. This method of arranging a plurality of amplifying stages is here termed stagger-damping.

It is often thought that getting the maximally fiat selectivity curve shown in Fig. 5 having the form 571 /5Tn 4n is the absolute value of the product a a 5 2:26 sin '11:) 5 2226 sin 1% my 55 J .1 a 4n .7

6 +jx25 sin Each factor of Equation E has the form of Equation B, thus the first factor of Equation E, for example, may be realized by a double-tuned circuit loaded on one side only and satisfying Therefore when considering each successive stage 70 of a stagger-damped amplifier having n serially connected stages, the Q for each successive stage should satisfy the relationship where y for each successive stage equals a term in an arithmetic series of odd integers beginning with 1 for the first stage and ending with (2n1) in the nth stage.

Observe the following two very convenient features of this stagger-damping scheme:

(a) All the transformers have the same coeflflcient of coupling, which means that only one transformer type is needed throughout and the only circuit difference from one stage to another is in the value of the shunting resistor.

(b) The coefficient of coupling is the ratio of desired overall bandwidth to center frequency.

While there has been described hereinabove what is at present considered to be a preferred embodiment of this invention, it will be obvious to those skilled in the art that various changes and modifications may be made therein without departing from the scope of the invention as set forth in the appended claims.

The invention claimed is:

1. In an electronic amplifier a plurality of n serially connected stages, each of said stages being tuned to a resonant frequency by means of two tuned coupled resonant circuits one of which is loaded, each of said stages having a coeificient of coupling 70 between said resonant circuits, said loading of each stage having the value such that the quality factor, Q, which is equal to woRC, is approximately equal to 210 sin with y equal to an odd integer, beginning with one and ending with (Zn-1), 010 is equal to 21:- times the resonant frequency of said circuits, R is the equivalent shunt resistance in said loaded circuit and C is equal to the equivalent shunt capacitance of said loaded circuit.

2. An electron amplifier including n cascaded stages each of said stages being tuned to a resonant frequency ft) by means of two resonant circuits, one of which is loaded, the coefiicient of coupling is for each of these stages being equal to 6 where 6 is the ratio of the overall bandwidth of said amplifier in cycles per second to f0 in cycles per second, and the quality factor of each of said stages is equal to values being a series of successive odd integers, beginning with one and ending with (Zn-1),

said amplifier having an overall selectivity voltage curve of the form 4m where X=2(wwo), w='21r times the frequency of the input signal to said amplifier in cycles per second and wo=21rfo.

3. In an electronic amplifier a plurality of n serially connected stages, each of said stages being tuned to a resonant frequency by means of two tuned coupled resonant circuits, each of said stages having a coeificient of coupling is between said resonant circuits, said loading of each stage having a value such that the ratio of the quality factor for that stage to the quality factor that would give transitional coupling is yr 2 sin where y is a series of successive odd integers, beginning with one and ending with (212-1).

4. In an electronic amplifier a plurality of serially connected double tuned amplifier stages, the coupling between successive stages being a constant determined by the ratio of the desired bandwidth at transitional coupling to the desired center frequency, one of the resonant circuits in each of said stages being loaded so that the damping of each stage has a different value, the damping of some of said stages being greater than the value of damping necessary to give transitional coupling and the damping of the remainder of said stages being less than the value of damping necessary to give transitional coupling.

5. An amplifier in accordance with claim 4 wherein the damping of each of said stages is a function of the number of stages in said amplifier and the damping of each successive stage differs by the reciprocal of the sine function of the odd integers of an arithmetic series.

HENRY WAILMAN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS 328,575 Great Britain Apr, 29, 1930 

